Rewrite as a simplified fraction. ${1.2\overline{14} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1214.1414...\\ 10x &= 12.1414...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1202}$ ${x = \dfrac{1202}{990}} $ ${x = \dfrac{601}{495}} \text{or} {1 \dfrac{106}{495}}$